YES
Time: 0.001465
TRS:
 {g(h x, y) -> h g(x, y),
  g(h x, y) -> h f(x, y),
    f(x, y) -> g(x, y)}
 DP:
  DP:
   {g#(h x, y) -> g#(x, y),
    g#(h x, y) -> f#(x, y),
      f#(x, y) -> g#(x, y)}
  TRS:
  {g(h x, y) -> h g(x, y),
   g(h x, y) -> h f(x, y),
     f(x, y) -> g(x, y)}
  EDG:
   {(g#(h x, y) -> f#(x, y), f#(x, y) -> g#(x, y))
    (f#(x, y) -> g#(x, y), g#(h x, y) -> g#(x, y))
    (f#(x, y) -> g#(x, y), g#(h x, y) -> f#(x, y))
    (g#(h x, y) -> g#(x, y), g#(h x, y) -> g#(x, y))
    (g#(h x, y) -> g#(x, y), g#(h x, y) -> f#(x, y))}
   SCCS (1):
    Scc:
     {g#(h x, y) -> g#(x, y),
      g#(h x, y) -> f#(x, y),
        f#(x, y) -> g#(x, y)}
    SCC (3):
     Strict:
      {g#(h x, y) -> g#(x, y),
       g#(h x, y) -> f#(x, y),
         f#(x, y) -> g#(x, y)}
     Weak:
     {g(h x, y) -> h g(x, y),
      g(h x, y) -> h f(x, y),
        f(x, y) -> g(x, y)}
     SPSC:
      Simple Projection:
       pi(f#) = 0, pi(g#) = 0
      Strict:
       {g#(h x, y) -> f#(x, y),
          f#(x, y) -> g#(x, y)}
      EDG:
       {(f#(x, y) -> g#(x, y), g#(h x, y) -> f#(x, y))
        (g#(h x, y) -> f#(x, y), f#(x, y) -> g#(x, y))}
       SCCS (1):
        Scc:
         {g#(h x, y) -> f#(x, y),
            f#(x, y) -> g#(x, y)}
        SCC (2):
         Strict:
          {g#(h x, y) -> f#(x, y),
             f#(x, y) -> g#(x, y)}
         Weak:
         {g(h x, y) -> h g(x, y),
          g(h x, y) -> h f(x, y),
            f(x, y) -> g(x, y)}
         SPSC:
          Simple Projection:
           pi(f#) = 0, pi(g#) = 0
          Strict:
           {f#(x, y) -> g#(x, y)}
          EDG:
           {}
           SCCS (0):
            
            Qed